agree with aid and margy
the next important issue is that your wife fusses at you because she has a valid point, then you get your feelings hurt.
Maturity in this area will come about when you get your feelings hurt - may be even valid because you were frustrated and trying to help.......then go back calmly and say- "let's sit down quietly and discuss WHAT TO DO NEXT TIME>"
My first husband was like this- he would think I didn't appreciate him but never would talk it through which is also frustrating-
He was a math teacher and the best way I could explain was this analogy:
Imagine a student is working a math problem over and over and over- using the wrong formula. Would you tell the student to just keep working it the same way- he will eventually solve the problem- noooooo- you go over alternative formulas and try to change the answer by the way you work the problem. He eventually gave up without trying and left our little home. that is not a man! That is a little frustrated boy.
Good men have to work at it- I am sure you are a good man and a wonderful father in the making- it just takes communication between you all.
It does sound as if you get on their case a lot and whilst you should be able to speak how you feel you could try to cut them some slack, we have all burnt fry pans havent we, thats no biggy he was trying to do something, and how does moving chairs around make you so upset, it is possible that your wife has a valid point. Focus on their positive side and praise them when you see them doing something right, get involved with sports and outside activities, get to like them, you will also then have a happy wife, its in your hands dwell on positive behavior not what you think is negative. Good Luck I know its not easy.
in regards to your son, have you sat him down and told him how much your new wife means to you, maybe he needs to how you feel. With your step sons, have a talk to your wife and come up with a plan of chores they need to complete each week, for example, they need to clean their rooms every Saturday morning, and H/W needs to be completed every second afternoon etc. hopefully you will both come to an agreement on whats sufficient for them. Ask her if she would be prepared to put it all in place, and then you can assist in enforcing them. it's always hard when you enter a family unit and feeling like the odd one out. Also make sure you have some fun with them, take them out and kick a soccer ball with them, that way you will be able to develop a bit more of a relationship with them. just make sure your not the one doing all the discipline either. :)